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Question 1. System of Linear Equations.
Solve the following system of linear equations by using Determinant Method:
Question 2. Matrix Algebra
Compute each of the following matrices:
a) A+B
b) C-D
c) CD
d) (CD)T
e) Verify that (CD)T = DTCT
f) Verify that (A+B)T = AT+BT
Question 3. Graphing Strategy
f(x) = -x3 + 27x
a) Find the domain of the function.
b) Find x and y intercepts.
c) Find the stationary points for and determine the intervals where is increasing and decreasing.
d) Determine the minimum and maximum value of the function.
e) Sketch the graph.
Assume that the average annual salary for a worker in the United States is $27,500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,250. Find the following:
A solution was prepared by mixing 4.00 ml 0.20 M NH3, 1.00 ml of 0.20 M HCl, and 5.00 ml of water. Calculate the concentration of NH3 and NH4+ in the final diluted solution.
Find the velocity of the rock after one second.
Find a solution of the differential equation that satisfies the initial condition y(1) = 3.
Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and on a bearing of N 23°E from the eastern station. How far is the balloon from the western station?
Determine the steady-state probabilities for this transition matrix algebraically and explain what they mean.
Two cars start moving from the same point. one travels south at 30 mi/h and the other travels west at 70 mi/h. At what rate is the distance between the cars increasing 2 hours later?
How do I relate the relationship between geometry and abstract algebra to how the symmetries of a square are conceptualized as the dihedral group of 8?
150 members indicated that they plan to attend the next Summer Olympic Games, and 90 indicated that they plan to attend the next Winter Olympic Games. How many members of the club plan to attend.
the revenue and cost functions for producing and selling quantity x for a certain production facility are given
What four steps should be used in evaluating expressions? Can these steps be skipped or rearranged? Explain your answers.
At an interest rate of 12%, the six-year discount factor is .507. How many dollars is $.507 worth in six years if invested at 12%?
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